Simplify; express your answer in exponential form. Assume $t\neq 0, q\neq 0$. $\dfrac{{(t^{4})^{-3}}}{{(t^{5}q^{-2})^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{4}}$ to the exponent ${-3}$ . Now ${4 \times -3 = -12}$ , so ${(t^{4})^{-3} = t^{-12}}$ In the denominator, we can use the distributive property of exponents. ${(t^{5}q^{-2})^{2} = (t^{5})^{2}(q^{-2})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(t^{4})^{-3}}}{{(t^{5}q^{-2})^{2}}} = \dfrac{{t^{-12}}}{{t^{10}q^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{-12}}}{{t^{10}q^{-4}}} = \dfrac{{t^{-12}}}{{t^{10}}} \cdot \dfrac{{1}}{{q^{-4}}} = t^{{-12} - {10}} \cdot q^{- {(-4)}} = t^{-22}q^{4}$.